medium difficulty6 min

Choosing correct ratio from a situation

Choosing the correct ratio from a situation means selecting the trigonometric ratio that matches the given sides or the required unknown in a word problem.

In one line: Choose the ratio by side match, not by memory alone.

Practice This Concept

Understand it

In applied questions, the diagram or description tells you which side is known and which side is needed. The correct ratio is not chosen by guesswork. It is chosen by matching the situation to opposite, adjacent, and hypotenuse with respect to the given angle.

Example

If a ladder makes an angle with the ground and the height reached on the wall is needed, sine or tangent may be used depending on the sides given.

Formula and rule

Match the known and required sides with the angle: sine uses opposite and hypotenuse, cosine uses adjacent and hypotenuse, tangent uses opposite and adjacent.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

If a pole is vertical and the ground distance is known with the angle of elevation, tan can be used to connect height and base directly.

Method you can reuse

1Convert the situation into a right triangle.
2Mark the angle of interest.
3Identify known and unknown sides.
4Pick the ratio that connects them directly.
5Solve the equation.

Sketch it in your answer

Draw the situation as a right triangle whenever possible. Mark the angle and label the given sides before choosing any ratio.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A ladder problem gives the length of the ladder and the height reached on the wall. Which ratio is often most direct?

Think first, then show answer

The most direct ratio is usually sine, because height is opposite the ground angle and the ladder is the hypotenuse. The exact choice still depends on the angle and the given sides.

Common wrong answer

A common wrong answer is to use a ratio that includes an extra side and makes the equation longer than needed.

Don't mix this up

Students often choose a ratio only because it sounds familiar, not because it matches the sides in the question.

Exam tip

First decide the angle, then decide whether the question uses opposite, adjacent, or hypotenuse.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

CBSE may ask word problems on height and distance, ladder problems, angle of elevation, or choose-the-ratio questions from a diagram.

1
Enough for 1 mark
Choosing the correct ratio from a situation means selecting the trigonometric ratio that matches the given sides or the required unknown in a word problem.
2
Add for 2 marks
Example: If a ladder makes an angle with the ground and the height reached on the wall is needed, sine or tangent may be used depending on the sides given.
3
Add for 3 marks
The correct ratio is not chosen by guesswork.

MCQ Quiz

Practice this concept with focused MCQs

Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.

10 MCQs5 MinutesInstant Results